Decoding the structure near the $\pi^+\pi^-$ mass threshold in $\psi(3686) \rightarrow J/\psi \pi^+\pi^-$ decays

TL;DR

This paper analyzes the dipion transition in $\psi(3686) ightarrow J/ e{psi} \pi^+\pi^-$ decays using dispersion theory, explaining the near-threshold structure without extra resonances and assessing the impact of exotic states.

Contribution

It introduces a model-independent dispersion approach to describe the near-threshold structure in $\psi(3686)$ decays, avoiding the need for additional resonance states.

Findings

Reproduces the near-threshold structure without extra resonances.

Helicity-flip amplitude is crucial for the dip.

Virtual exchange of $Z_c(3900)$ slightly improves fit.

Abstract

In light of recent high-precision data taken by the BESIII Collaboration, we reconsider the dipion transition $\psi(3686) \rightarrow J/\psi \pi^+\pi^-$. The strong pion-pion final-state interactions are taken into account model-independently by using dispersion theory. We find that we can reproduce the substructure near the $\pi^+\pi^-$ threshold observed experimentally without introducing an extra resonance state. While a helicity-flip amplitude plays an important role for the formation of the dip in the invariant-mass distribution, the virtual exchange of the charmoniumlike exotic $Z_c(3900)$ state improves the fit quality only slightly.